Slope and Equation of a line How to find the slop of a line? (x 1, y 1 ) (x 2, y 2 ) How to find the equation of a line? Sec 2.1: Rates of Change and.

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Presentation transcript:

Slope and Equation of a line How to find the slop of a line? (x 1, y 1 ) (x 2, y 2 ) How to find the equation of a line? Sec 2.1: Rates of Change and Tangents to Curves

The word tangent is derived from the Latin word tangens, which means “touching.” Tangent line Secant line a line joining two points of a curve is a secant to the curve. slope of a curve at a point P on the curve? the slope of the tangent at P. What is the difference ?? Lines?? Sec 2.1: Rates of Change and Tangents to Curves

Is it possible that a line could be tangent and secant in the same time Sec 2.1: Rates of Change and Tangents to Curves

Secant line and Tangent line How to find the slope of these lines ?? Tangent line Sec 2.1: Rates of Change and Tangents to Curves

Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

Q tangent line Example : Find the slope of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves

Q tangent line Example : Find the slope of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves

1.5(1.5,2.25) (1.2,1.44) (1.2,1.21) (1.01,1.0201)2.01 Example : Find the slope of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves

1 1 x X^2 Example : Find the slope of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves

tangent line secant line Slope of the tangent line = 2.0 Sec 2.1: Rates of Change and Tangents to Curves

tangent line secant line Equation of the tangent line Slope = 2.0 point = (1, 1) Example : Find the equation of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves

tangent line secant line Sec 2.1: Rates of Change and Tangents to Curves

as means Sec 2.1: Rates of Change and Tangents to Curves

EXAM-1 TERM-081

Average Speed Instantaneous Speed Average Rates of Change Instantaneous Rates of Change The Derivative as a Rate of Change 3.4 Sec 2.1: Rates of Change and Tangents to Curves Q(2.1):Rates of Change and Tangents to Curves Start: September 2, :30 AM End: September 7, :30 PM